Approximate Decoupling of the Equations of Motion of Linear Second Order Systems

One common procedure in solving a normalized damped linear second order system with nonzero off-diagonal damping elements is to replace the normalized damping matrix by a selected diagonal matrix. The extent of approximation introduced by this method of decoupling the system is evaluated and tight upper bounds on the norm of errors are derived. Moreover, it is shown that when the normalized damping matrix is diagonally dominant, decoupling the system by neglecting the off-diagonal elements indeed minimizes the error upper bound.